Battery temperature detection

ABSTRACT

A method and a temperature detection circuit are disclosed. An example of the method includes driving an alternating current with a first frequency into a battery and detecting an imaginary part of a battery impedance at the first frequency; driving an alternating current with a second frequency different from the first frequency into the battery and detecting an imaginary part of the battery impedance at the second frequency; and calculating an intercept frequency at which the imaginary part equals a predefined value at least based on the imaginary part obtained at the first frequency and the imaginary part obtained at the second frequency.

TECHNICAL FIELD

This disclosure relates in general to detecting the temperature of abattery. In particular, this disclosure relates to a sensor-less batterytemperature detection.

BACKGROUND

Detecting or measuring the temperature of a battery, such as alithium-ion (Li-ion) battery, may include driving an alternating currentwith a varying frequency into the battery, measuring a complex impedanceof the battery at each frequency of the current in order to detect thefrequency at which an imaginary part of the impedance is zero, anddetecting the temperature based on this frequency at which the imaginarypart of the impedance is zero. This method, which is known as ZIF (ZeroIntercept Frequency) method is based on the fact that the imaginary partof the battery impedance is dependent on the temperature in such a waythat at a given temperature the imaginary part of the battery impedanceof batteries of a certain type intercepts zero at essentially the samefrequency. This frequency where the imaginary part of the impedanceintercepts zero is referred to as ZIF. Usually, the ZIF of a certainbattery type is the higher the lower the temperature is. For eachbattery type the ZIF can be detected at different known temperatures (bythe battery manufacturer, for example) and each of these knowntemperatures can be associated with a respective ZIF so as to obtain aplurality of ZIF-temperature pairs. At an application site of thebattery, the temperature can be detected by detecting the ZIF, whereinthe temperature is the temperature associated with the detected ZIF.

In some types of batteries, such as high quality automotive batteries,the ZIF, especially at high temperatures, may occur at relatively lowfrequencies. Measurements at low frequencies, however, may be affectedby noise (interferences) such as interferences generated by an electricmotor in an automobile. Such interferences may make measurements at lowfrequencies less reliable than measurements at higher frequencies.

Another approach, which is referred to as NZIF (Non Zero InterceptFrequency), is to detect those frequencies where the imaginary part ofthe battery impedance equals a predefined value different from zero.Each of these frequencies is associated with a certain temperature sothat, similar to the ZIF method, the temperature can be detected bydetecting the frequency where the imaginary part of the batteryimpedance equals the predefined value. A frequency where the imaginarypart intercepts the predefined value different from zero is referred toas NZIF. The predefined value can be selected such that the NZIFs arehigher than the ZIFs so that interferences are less likely to occur inthe NZIF method. The NZIF method, however, requires a precise detectionor measurement of the imaginary part of the battery impedance in orderto detect when the imaginary part equals the predefined value.

Further, in both the ZIF method and the NZIF method, measurements at aplurality of different frequencies are required. This is time consuming.

There is therefore a need for an improved sensor-less batterytemperature detection.

SUMMARY

One example relates to a method. The method includes driving analternating current with a first frequency into a battery and detectingan imaginary part of a battery impedance at the first frequency, drivingan alternating current with a second frequency different from the firstfrequency into the battery and detecting an imaginary part of thebattery impedance at the second frequency, and calculating an interceptfrequency at which the imaginary part equals a predefined value at leastbased on the imaginary part obtained at the first frequency and theimaginary part obtained at the second frequency.

Another example relates to a temperature detection circuit. Thetemperature detection circuit is configured to drive an alternatingcurrent with a first frequency into a battery and detect an imaginarypart of a battery impedance at the first frequency, drive an alternatingcurrent with a second frequency different from the first frequency intothe battery and detect an imaginary part of the battery impedance at thesecond frequency, and calculate an intercept frequency at which theimaginary part equals a predefined value at least based on the imaginarypart obtained at the first frequency and the imaginary part obtained atthe second frequency.

BRIEF DESCRIPTION OF THE DRAWINGS

Examples are explained below with reference to the drawings. Thedrawings serve to illustrate certain principles, so that only aspectsnecessary for understanding these principles are illustrated. Thedrawings are not to scale. In the drawings the same reference charactersdenote like features.

FIG. 1 schematically illustrates an arrangement with a battery andtemperature detection circuit connected to the battery and configured todetect a temperature of the battery;

FIGS. 2A-2D show different examples of a battery;

FIG. 3 schematically illustrates how an imaginary part of a complexbattery impedance is dependent on a battery temperature and a frequencyof a current driven into the battery;

FIG. 4 illustrates one example of how a frequency at which the imaginarypart of the battery equals a predefined value can be obtained based onimaginary parts of the battery impedance obtained at two differentfrequencies;

FIG. 5 shows a flow diagram that illustrates one example of a method fordetecting a battery temperature based on measuring the imaginary part ofthe battery impedance at two different frequencies;

FIG. 6 illustrates one example of how a frequency at which the imaginarypart of the battery equals a predefined value can be obtained based onimaginary parts of the battery impedance obtained at more than twodifferent frequencies;

FIG. 7 shows a temperature detection circuit according to one example;

FIG. 8 shows a temperature detection circuit according to anotherexample;

FIG. 9 shows a temperature detection circuit according to yet anotherexample;

FIG. 10 shows an arrangement with a plurality of batteries connected inseries and a plurality of battery detection circuits;

FIG. 11 shows an arrangement with a plurality of batteries connected inseries and one temperature detection circuit; and

FIG. 12 shows an arrangement with a plurality of batteries connected inseries and a temperature detection circuit according to a furtherexample.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings. The drawings form a part of the description andfor the purpose of illustration show examples of how the invention maybe used and implemented. It is to be understood that the features of thevarious embodiments described herein may be combined with each other,unless specifically noted otherwise.

FIG. 1 schematically illustrates an arrangement with a battery 1 and atemperature detection circuit 2. The temperature detection circuit isconnected to a first battery node 11 and a second battery node 12 of thebattery 1 and is configured to detect a temperature of the battery 1 ina way explained in further detail herein below.

The battery 1 is a lithium-ion (Li-ion) battery, for example. Thebattery 1 includes at least one battery cell. Some examples of how thebattery 1 may be implemented are illustrated in FIGS. 2A to 2D.

Referring to FIG. 2A, the battery 1 may include one battery cell 1 ₁₁connected between the first battery node 11 and the second battery node12. According to another example shown in FIG. 2B, the battery 1includes a plurality of battery cells 1 ₁₁, 1 ₂₁, 1 _(n1) connected inseries between the first battery node 11 and the second battery node 12.According to another example shown in FIG. 2C, the battery 1 includes aplurality of battery cells 1 ₁₁, 1 ₁₂, 1 _(1m) connected in parallelbetween the first battery node 11 and the second battery node 12.According to yet another example shown in FIG. 2D, the battery oneincludes a series circuit with two or more parallel circuits, whereineach of these parallel circuits includes two or more battery cells 1 ₁₁,1 ₁₂, 1 _(1m), 1 _(n1), 1 _(n2), 1 _(nm).

Detecting the battery temperature by the temperature detection circuit 2shown in FIG. 1 includes driving an alternating current i(f,t) via thebattery nodes 11, 12 into the battery 1 and measuring a compleximpedance Z(f) of the battery 1. The current i(f,t) is also referred toas input current in the following. Measuring the impedance Z(f) includesmeasuring a voltage v(f,t) between the battery nodes 11, 12. When thecurrent i(f,t) driven into the battery 1 is an alternating current thevoltage v(f,t) between the battery nodes 11, 12 is an alternatingvoltage.

As used herein, an “alternating current” is a current that includes analternating current component and that, additionally, may include adirect current (DC) offset. According to one example, the alternatingcurrent component is a sinusoidal current component. In the following,an alternating current with a sinusoidal current component is referredto as sinusoidal current. A sinusoidal input current i(f,t) is given byi(f,t)=I _(DC) +I ₀·sin(ωt)  (1),where I₀ is an amplitude of the sinusoidal current component, ω=2π·f,and I_(DC) is the optional DC offset. As used herein, “driving a currentinto the battery” may include driving only a positive current thatcharges the battery, only a negative current that discharges thebattery, or alternatingly a positive current and a negative current. Ifin the example given in equation (1) the DC offset I_(DC) is zero(I_(DC)=0), there are time periods when the current is positive so thatthe battery 1 is charged and time periods when the current is negativeso that the battery is discharged, wherein over each period of thesinusoidal input current i(f,t) the charging state of the battery 1 doesnot change. According to another example, the DC offset I_(DC) isdifferent from zero and selected such that the input current is eitheronly positive or only negative, wherein the current direction of theinput current i(f,t) can be adjusted by selecting the sign (positive ornegative) of the DC offset I_(DC).

Using a sinusoidal current as the alternating input current i(f,t) isonly an example. Alternating currents with alternating currentcomponents that have a waveform different from a sinusoidal waveform maybe used as well. Examples of these other types of waveforms include, butare not restricted to, a rectangular waveform, a triangular waveform, asine square waveform, or the like.

When the input current i(f,t) is a sinusoidal current as given inequation (1) the voltage v(f,t) between the battery nodes 11, 12 is analternating voltage as follows:v(f,t)=V ₀ +Z ₀·(I _(DC) +I _(O)·sin(ωt+φ))  (2),where Z₀ is the magnitude of a complex impedance of the battery 1, φ isa phase shift introduced by the complex impedance of the battery.Further, V₀ is an optional offset of the battery voltage v(f,t). Thisoffset V₀ represents a charging state of the battery 1, that is V₀ isthe voltage that can be measured between the battery nodes 11, 12 whenno input current (i(f,t)=0) is driven into the battery 1. In general,the complex impedance Z(f) of the battery 1 can be written asZ(f)=Z ₀ ·e ^(jφ)=Re{Z(f)}+j·Im{Z(f)}=Z ₀·cos φ+j·Z ₀·sin φ  (3),where Re{Z(f)} is the real part and Im{Z(f)} is the imaginary part ofthe complex battery impedance Z(f), and j is the imaginary unit. Thereal part Re{Z(f)} can also be referred to as resistance and theimaginary part Im{Z(f)} can also be referred to as reactance of thebattery 1. The impedance Z(f) is dependent on the frequency f of theinput current i(f,t), so that the magnitude Z₀ and the phase φ of theimpedance Z(f) are also dependent on the frequency (are a function ofthe frequency), that is, Z₀=Z₀(f) and φ=φ(f).

It is known that the imaginary part Im{Z(f)} of the impedance Z(f) isdependent on the frequency f of the input current i(f,t) and the batterytemperature T. This is schematically illustrated in FIG. 3. For thepurpose of illustration, FIG. 3 illustrates three curves 101, 102, 103,wherein each of these curves represents the imaginary part Im{Z(f)} ofthe impedance Z(f) dependent on the frequency f of the input currenti(f,t) at a certain temperature T1, T2, T3. As can be seen from FIG. 3the imaginary part Im{Z(f)} of the impedance Z(f), at each of thetemperatures T1, T2, T3 shown in FIG. 3, is essentially linearlydependent on the frequency f.

The ZIF method explained above detects the frequency at which theimaginary part Im{Z(f)} is zero. Those frequencies are referred to ZIF1,ZIF2, ZIF3 in FIG. 3. Each of these frequencies, which are also referredto as zero intercept frequencies (ZIFs), is associated with onetemperature (T1, T2, T3 in FIG. 3) so that based on these ZIFs thebattery temperature can be detected. In the NZIF method explained abovethe frequency is detected where the imaginary part Im{Z(f)} equals apredefined value V that is different from zero. This frequency isreferred to as non-zero intercept frequency (NZIF). In the example shownin FIG. 3 the NZIFs are referred to as NZIF1, NZIF2, NZIF3. Both, theZIF method and the NZIF method, however, require that the imaginary partIm{Z(f)} of the battery impedance Z(f) is measured at a plurality ofdifferent frequencies f. This is time consuming.

An alternative approach to detect the battery temperature is illustratedin FIG. 4. A flow chart of the method illustrated in FIG. 4 is shown inFIG. 5. Referring to FIGS. 4 and 5, the method includes determining animaginary part Im{Z(f₁)} of a battery impedance Z(f₁) at a firstfrequency f1 (in step S101 shown in FIG. 5), and determining theimaginary part Im{Z(f₂)} of the battery impedance Z(f₂) at a secondfrequency f2 (in step S102 shown in FIG. 5). In this context, “at afirst frequency f1” means when driving an alternating input currenti(f_(1,t)) with the first frequency f₁ into the battery 1, and “at asecond frequency f2” means when driving an alternating input currenti(f_(2,t)) with the second frequency f₂ into the battery 1. Further, themethod includes (in step S103 shown in FIG. 5) calculating a frequencyf₀ where the imaginary part Im{Z(f₀)} of the battery impedance equals apredefined value P based on the imaginary parts Im{Z(f₁)}, Im{Z(f₂)}obtained at the first frequency f₁ and the second frequency f₂.According to one example, the predefined value P is zero (P=0). If thepredefined value P is zero the frequency f₀ is a zero interceptfrequency (ZIF) as it defines a frequency at which the imaginary part iszero. As this ZIF is obtained by a calculation, such as an extrapolationbased on two measured imaginary parts Im{Z(f₁)}, Im{Z(f₂)}, thefrequency f₀ may be referred to as extrapolated zero intercept frequency(EZIF).

Based on the calculated frequency f₀ the battery temperature can bedetected (in step S104 in FIG. 5). Determining the battery temperaturebased on the frequency f₀ may include looking up the temperature in alook-up table that holds a plurality of frequency-temperature pairs,wherein each of these frequency-temperature pairs includes a certaintemperature and an associated frequency. The “associated frequency” isthe frequency at which, at the certain temperature, the imaginary partof the battery impedance equals the predefined value P. Thesetemperature-frequency pairs are the same for each battery type so that alook-up table for each battery type may be generated (by the batterymanufacturer, for example) based on measurements applied to one or morebatteries of this type. Those measurements may include detecting theimaginary part of the battery impedance at a plurality of differentfrequencies and at a plurality of different (known) battery temperaturesand detecting, at each of the plurality of temperatures, the frequencyat which the imaginary part equals the predefined value P. During thesemeasurements, the battery temperature may be obtained using atemperature sensor arranged inside the battery.

In the following the imaginary part Im{Z(f₁)} obtained at the firstfrequency f₁ is briefly referred to as first imaginary part Im₁, and theimaginary part Im{Z(f₂)} obtained at the second frequency f₂ is brieflyreferred to as second imaginary part Im₂. Calculating the frequency f₀at which the imaginary part equals P based on the first imaginary partIm₁ and the second imaginary part Im₂ is based on the fact that, at onetemperature, the imaginary part of the battery impedance Z(f) isessentially linearly dependent on the frequency f, that is, theimaginary parts obtained at different frequencies are essentiallylocated on a straight line in a diagram that shows the imaginary partover the frequency, such as a diagram of the type shown in FIG. 3. Basedon this, the frequency f₀ may be calculated based on the first imaginarypart Im₁, the second imaginary part Im₂, the first frequency f₁, thesecond frequency f₂, and the predefined value P as follows:

$\begin{matrix}{f_{0} = {f_{1} - {\frac{{Im}_{1} - P}{{Im}_{2} - {Im}_{1}} \cdot {\left( {f_{2} - f_{1}} \right).}}}} & (4)\end{matrix}$This is based on the assumption that the imaginary part Im{Z(f)} of thebattery impedance can approximately be expressed by a linear function(first order function) as follows:

$\begin{matrix}{{{Im}\left\{ {Z(f)} \right\}} = {P + {\left( \frac{{Im}_{2} - {Im}_{1}}{f_{2} - f_{1}} \right) \cdot {f.}}}} & (5)\end{matrix}$

Calculating f₀ based on only two imaginary parts, such as the firstimaginary part Im₁ and the second imaginary part Im₂ explained above, isonly an example. According to another example, the method includesobtaining two or more imaginary parts Im₁, Im₂, Im_(n) at differentfrequencies f₁, f₂, f_(n), calculating a linear or non-linear functionof the imaginary part Im{Z(f)} based on these imaginary parts Im₁, Im₂,Im_(n) and, based on the linear function or the non-linear function,calculating the frequency where the imaginary part Im{Z(f)} equals P,that is, calculating f₀ so that Im{Z(f₀)}=P.

According to one example, a linear function is calculated based on theplurality of imaginary parts Im₁, Im₂, Im_(n). This is illustrated inFIG. 6. FIG. 6 shows n imaginary parts Im₁, Im₂, Im_(n) obtained atdifferent frequencies f₁, f₂, f_(n) and a straight line (drawn as dashedline) that represents the linear function based on which f₀ iscalculated. Just for the purpose of illustration, n=3 in the exampleshown in FIG. 6; any number higher than n=3 may be used as well. Thelinear function may be calculated based on a “least square method”(LSM). Such method is known so that no further explanations arerequired. According to another example (not shown), a non-linearfunction is calculated based on n, where n≥3, imaginary parts. Inparticular this example includes calculating a function of order n−1based on n imaginary parts as follows:Im{Z(f)}=a _(n) f ^(n) +a _(n-1) f ^(n-1) + . . . +a ₁ f+a ₀  (6),and calculating f₀ based on this function such that Im{Z(f₀)}=P. It iscommonly known how based on n values, such as n imaginary partsexplained above, a non-linear function of order n−1 can be calculated.Thus, no further explanations are required in this regard.

In the method explained with reference to FIGS. 4 and 5, the imaginarypart of the battery impedance is to be detected (measured) only at twodifferent frequencies, the first frequency f₁ and the second frequencyf₂ explained before, wherein, referring to FIG. 6, more than twomeasurements at different frequencies f₁, f₂, f_(n) may be performed.The at least two frequencies f₁, f₂, f_(n) may be chosen arbitrarily. Inparticular, these frequencies may be chosen from a frequency range that,usually, is not effected by interferences in an application environmentof the battery. According to one example, the at least two frequenciesf₁, f₂, f_(n) are each selected from a range of between 100 Hz and 10kHz, in particular between 1 kHz and 10 kHz.

FIG. 7 shows one example of a temperature detection circuit 2 that isconfigured to detect the battery temperature based on one of the methodsexplained with reference to FIGS. 4, 5 and 6. FIG. 7 shows a blockdiagram of the temperature detection circuit 2. It should be noted thatthis block diagram illustrates the functional blocks of the temperaturedetection circuit 2 rather than a specific implementation. Thosefunctional blocks can be implemented in various ways. According to oneexample, these functional blocks are implemented using dedicatedcircuitry, such as analog circuits, digital circuits or analog anddigital circuits. According to another example, the temperaturedetection circuit 2 is implemented using hardware and software. Forexample, the temperature detection circuit 2 includes a microcontrollerand software running on the microcontroller.

Referring to FIG. 7, the temperature detection circuit 2 includes acurrent source 21 configured to provide a direct current with a currentlevel I₀. A modulator 22 connected downstream the current source 21 isconfigured to modulate the current I₀ provided by the current source 21with a first alternating signal s1(ωt). Optionally, the DC offset I_(DC)is added to an output signal of the modulator 22 by an optional adder28. The current i(f,t) driven into the battery 1 is available at anoutput of the modulator 22 or an output of the adder 28. In general,this current i(f,t) is given byi(f,t)=I _(DC) +I ₀ ·s1(ωt)  (5).According to one example, the first alternating signal s1(ωt) is asinusoidal signal, so that the input current i(f,t) is given by equation(1). This, however, is only an example. Other alternating signalwaveforms such as a rectangular waveform may be used as well. The firstalternating signal s1(ωt) is generated by a modulation signal generator23 in accordance with a frequency signal S_(f) provided by a control andcalculation circuit 27. The frequency signal S_(f) defines the frequencyof the alternating signal s1(ωt) provided by the modulation signalgenerator 23.

Referring to FIG. 7, the temperature detection circuit 2 furtherincludes a measurement unit 24 coupled to the battery nodes 11, 12 andconfigured to measure the battery voltage v(f,t). An output signalm(f,t) provided by the measurement circuit 24 is proportional to thebattery voltage v(f,t) and is given bym(f,t)=A ₀ ·v(f,t)  (6)where A₀ is an amplification factor (gain) of the measurement unit 24. Ademodulator 25 receives the measurement signal m(f,t) from themeasurement unit 24 and a second alternating signal s2(ωt). The secondalternating signal s2(ωt) is also generated by the modulation signalgenerator 23 and is a phase shifted version of the first alternatingsignal s1(ωt). According to one example a phase shift between the firstalternating signal s1(ωt) and the second alternating signal s2(ωt) is90° (=π/2), so that

$\begin{matrix}{{s\; 2\left( {\omega\; t} \right)} = {s\; 1\left( {{\omega\; t} \mp \frac{\pi}{2}} \right)}} & (7)\end{matrix}$According to one example, s1(ωt)=sin(ωt) and s2(ωt)=cos(ωt). In thisexample, an output signal s25(f,t) of the demodulator 25 is given bys25(f,t)=A ₀ ·v(f,t)·cos(ωt)==A ₀·[V ₀ +Z ₀·(I _(DC) +I ₀·sin(ωt+φ))]·cos(ωt)  (8a).Using trigonometrical formulae, equation (8a) can be written as

$\begin{matrix}{\left. {{s\; 25\left( {f,t} \right)} = {A_{0} \cdot \left\lbrack {{\left( {V_{0} + {Z_{0} \cdot I_{DC}}} \right){\cos\left( {\omega\; t} \right)}} + {\frac{Z_{0} \cdot I_{0}}{2}\left( {\sin\left( {{2\omega\; t} + \varphi} \right)} \right)} + {\sin(\varphi)}} \right)}} \right\rbrack.} & \left( {8b} \right)\end{matrix}$Referring to FIG. 7, the demodulator output signal s25(f,t) is receivedby a low pass filter 26. A cut of frequency of this low pass filter 26is such that alternating components (that is, components with thefrequency ωt or multiples of this frequency) of the demodulator outputsignal s25(f,t) are filtered out, so that an output signal of the lowpass filter 26 is given by

$\begin{matrix}{{{s\; 26\left( {f,t} \right)} = {A_{0} \cdot \left\lbrack {\frac{Z_{0}I_{0}}{2} \cdot {\sin(\varphi)}} \right\rbrack}},} & (9)\end{matrix}$which, referring to equation (3) is a scaled version of the imaginarypart of the battery impedance Z(f). The low pass filter may be any typeof low pass filter. According to one example, the low pass filter is aCIC (Cascaded Integrator Comb) filter.

Referring to FIG. 7, The low pass filter output signal s26(f,t) isreceived by the control and calculation circuit 27. The control andcalculation circuit 27 is configured to control the modulation signalgenerator 23 such that in a first phase of the temperature detectionprocess the modulation signal generator generates the first and secondalternating signals s1(ωt), s2(ωt) with the first frequency f₁. In thisfirst phase, the low pass filter output signal s26(f,t) received by thecontrol and calculation circuit 27 is proportional to the firstimaginary part Im₁ of the battery impedance, wherein a proportionalityfactor

$\frac{A_{0} \cdot I_{0}}{2}$is defined by the gain A₀ of the measurement unit 24. In a second phaseof the temperature detection process, the control and calculationcircuit 27 controls the modulation signal generator 23 to generate thefirst and second alternating signals s1(ωt), s2(ωt) with the secondfrequency f₂. Thus, in second phase the low pass filter signal s26(f,t)received by the control and calculation circuit 27 is proportional tothe second imaginary part Im₂ of the battery impedance. Based on theseimaginary parts that are proportional to the first and second imaginaryparts Im₁, Im₂ the control and calculation circuit 27 calculates thefrequency f₀ at which the imaginary part of the battery impedance equalsthe predefined value P. The control and calculation circuit 27 maycalculate f₀ based on equation (4), wherein the low pass filter outputsignal received by control and calculation circuit 27 may be divided bythe proportionality factor

$\frac{A_{0} \cdot I_{0}}{2}$before applying equation (4) in order to calculate f₀.

If, for example, the predefined value P is zero (P=0) such division isnot required, that is, the scaled versions

$\frac{A_{0}I_{0}}{2}{\sin\left( {\varphi\left( f_{1} \right)} \right)}\mspace{14mu}{and}\mspace{14mu}\frac{A_{0}I_{0}}{2}{\sin\left( {\varphi\left( f_{2} \right)} \right)}$may be used in equation (4) instead of Im₁=sin(φ(f₁)) andIm₂=sin(φ(f₂)). The reason is that, if P=0, equation (4) can be writtenas

$\begin{matrix}{{f_{0} = {f_{1} - \frac{{Im}_{1}}{{Im}_{2} - {Im}_{1}}}}{{\cdot \left( {f_{2} - f_{1}} \right)},{and}}} & (10) \\{\frac{{Im}_{1}}{{Im}_{2} - {Im}_{1}} = {\frac{\frac{A_{0}I_{0}}{2}{Im}_{1}}{{\frac{A_{0}I_{0}}{2}{Im}_{2}} - {\frac{A_{0}I_{0}}{2}{Im}_{1}}}.}} & (11)\end{matrix}$For the same reason, the method, if P=0, is very robust if it comes tovariations of the amplification factor A of the measurement unit. Thosevariations may include variations either during operation of onetemperature detection circuit or different amplification factors indifferent temperature detection circuits.

According to one example, the control and calculation circuit 27 furtherincludes a look-up table and is configured to look up a temperatureassociated with the calculated frequency f₀, and to output a temperaturesignal S_(T) that represents the temperature associated with thecalculated frequency f₀.

The explanation provided above is based on the assumption that the onlyphase shift the amplifier output signal m(f,t) has relative to the firstalternating signal s1(ωt) is the phase shift φ resulting from thebattery 1. However, there may be an additional phase shift φ₀ resultingfrom the temperature measurement circuit 2 itself, that is, for example,the amplifier 24, the modulator 22 and the optional adder 28. Thus, theamplifier output signal m(f,t) may in fact be given bym(f,t)=A ₀·[V ₀ +Z ₀·(I _(DC) +I ₀·sin(ωt+φ ₀+φ))]  (12).The phase shift φ₀ introduced by the temperature measurement circuit 2may be compensated in various ways. Some examples are explained below.In two of these examples, the phase shift φ₀ is measured in acalibration step before the temperature measurement circuit 2 is used tomeasure the battery temperature. The calibration step may includecoupling an ohmic resistor instead of a battery 1 to the temperaturemeasurement circuit 2 and calculating the phase shift φ₀ based on thelow pass filter output signal s26(f,t) which, in the calibration step,is given by

$\begin{matrix}{{{s\; 26\left( {f,t} \right)} = {A_{0} \cdot \left\lbrack {\frac{R_{0}I_{0}}{2} \cdot {\sin\left( \varphi_{0} \right)}} \right\rbrack}},} & (13)\end{matrix}$where R₀ is a resistance of the resistor used in the calibration step.Based on equation (13), which is based on equation (9), the phase shiftφ₀ may be calculated by

$\begin{matrix}{\varphi_{0} = {{\arcsin\left( \frac{{2 \cdot s}\; 26\left( {f,t} \right)}{A \cdot {{}_{}^{}{}_{}^{}} \cdot I_{0}} \right)}.}} & (14)\end{matrix}$

According to one example that is illustrated in dashed lines in FIG. 7,the temperature measurement circuit 2 includes a phase shifter 29 thatreceives the second alternating signal s2(ωt) and provides a phaseshifted version s2(ωt+φ ₀) of the second alternating signal to thedemodulator 25, wherein the phase shifted version s2(ωt+φ ₀) of thesecond alternating signal takes into account the phase shift φ₀ measuredin the calibration process. The phase shift introduced by thetemperature measurement circuit may be dependent on the frequency sothat φ₀=φ₀(f). In this case, a calibration step may be performed atthose different frequencies f₁, f₂ of the input current i(f,t) at whichthe at least two imaginary parts Im₁, Im₂ are obtained in operation ofthe temperature measurement circuit. In each calibration step one phaseshift φ₀(f₁), φ₀(f₂) associated with the respective frequency f₁, f₂ isobtained and stored in the control and calculation circuit 27. In thiscase, during a temperature measurement operation of the temperaturemeasurement circuit 2, the phase shifter 29 receives the correct phaseshift information from the control and calculation circuit 27 in each ofthe at least two measurement phases in which the input current i(f,t)has different frequencies f1, f2.

FIG. 8 shows a modification of the temperature detection circuit 2 shownin FIG. 7. The temperature detection circuit shown in FIG. 8 isdifferent from the one shown in FIG. 7 in that it includes a firstdemodulator 25 _(I) and a second demodulator 25 _(Q) that each receivethe measurement signal m(f,t). A first low pass filter 26 _(I) isconnected downstream the first demodulator 25 _(I), and a second lowpass filter 26 _(Q) is connected downstream the second demodulator 25_(Q). The first demodulator 25 _(I) receives a third alternating signals1′(ωt) and the second demodulator 25 _(Q) receives the secondalternating signal s2(ωt). The third alternating signal s1′(ωt) and thesecond alternating signal s2(ωt) are selected such that there is a phaseshift of π/2 (=90°) between the third alternating signal s1′(ωt) and thesecond alternating signal s2(ωt). The third alternating signal s1′(ωt)may be in phase with the first alternating signal s1(ωt). This, however,is not mandatory. If there is a phase shift between the first signals1(ωt) and the third signal s1′(ωt) such phase shift can be consideredas part of the phase shift introduced by the temperature detectioncircuit and is compensated by the mechanism explained below. Accordingto one example, the third alternating signal s1′(ωt) and the secondalternating signal s2(ωt) have a sinusoidal waveform so that, forexample, s1′(ωt)=sin(ωt) and s2(ωt)=cos(ωt). In this case, outputsignals s25 _(I)(f,t), s25 _(Q)(f,t) of the demodulators 25 _(I), 25_(Q) are as follows:s25_(I)(f,t)=A ₀ ·v(f,t)·s1′(ωt)=A ₀ ·v(f,t)·sin(ωt)  (15a)s25_(Q)(f,t)=A ₀ ·v(f,t)·s2(ωt)=A ₀ ·v(f,t)·cos(ωt)  (15b).If the input current i(f,t) is a sinusoidal current, the firstalternating signal s1(ωt) and the third alternating signal s1′(ωt) maybe identical. If, for example, v(f,t) is in accordance with equation (2)and there is an additional phase shift φ₀ introduced by the temperaturedetection circuit 2 the demodulator output signals s25 _(I)(f,t), s25_(Q)(f,t) ares25_(I)(f,t)=A ₀·[V ₀ +Z ₀·(I _(DC) +I ₀·sin(ωt+φ ₀+φ))]·sin(ωt)  (16a)s25_(Q)(f,t)=A ₀·[V ₀ +Z ₀·(I _(DC) +I ₀·sin(ωt+φ ₀+φ))]·cos(ωt)  (16b).The low pass filters 26 _(I), 26 _(Q) are configured to filter signalcomponents with a frequency ωt and higher. Output signals s26 _(I)(f,t),s26 _(Q)(f,t), which are also referred to as inphase component V_(I) andquadrature component V_(Q) in the following, of these low pass filters26 _(I), 26 _(Q) are given by

$\begin{matrix}{{s\; 26_{I}\left( {f,t} \right)} = {V_{I} = {\frac{A_{0} \cdot Z_{0} \cdot I_{0}}{2}{\cos\left( {\varphi_{0} + \varphi} \right)}}}} & \left( {17a} \right) \\{{s\; 26_{Q}\left( {f,t} \right)} = {V_{Q} = {\frac{A_{0} \cdot Z_{0} \cdot I_{0}}{2}{{\sin\left( {\varphi_{0} + \varphi} \right)}.}}}} & \left( {17b} \right)\end{matrix}$

According to one example, the control and calculation circuit 27 isconfigured to divide the inphase and quadrature component by

$\frac{I_{0}}{2}$to obtains26₁′(f,t)=V _(I) ′=A ₀ ·Z ₀·cos(φ₀+φ)  (18a)s26_(Q)′(f,t)=V _(Q) ′=A ₀ ·Z ₀·sin(φ₀+φ)  (18b),wherein these signals (values) can be considered as the real part andthe imaginary part of a product of a complex impedance Z of the battery1 and a complex gain A of the amplifier 24. The complex gain also takesinto account the overall phase shift φ₀ introduced by the temperaturedetection circuit 2. Thus,V _(I) ′+jV _(Q) ′=A·Z=(A ₀ ·e ^(jφ) ⁰ )·(Z ₀ ·e ^(jφ))  (19),According to one example, the complex gain A, which includes themagnitude A₀ and the phase shift φ₀, is determined in one or morecalibration steps and stored in the control and calculation unit. Basedon A₀ and φ₀ and on V_(I)′ and V_(Q)′ the control and calculation unitcircuit 27 may calculate the magnitude Z₀ and phase φ of the batteryresistance Z as follows:

$\begin{matrix}{Z_{0} = \frac{\sqrt{\left( V_{I}^{\prime} \right)^{2} + \left( V_{Q}^{\prime} \right)^{2}}}{A_{0}}} & \left( {20a} \right) \\{\varphi = {{\arctan\left( \frac{V_{Q}^{\prime}}{V_{I}^{\prime}} \right)} - {\varphi_{0}.}}} & \left( {20b} \right)\end{matrix}$Referring to the above, the magnitude Z₀ and phase φ are dependent onthe frequency, that is, Z₀=Z₀(f) and φ=φ(f) so that the control andcalculation circuit 27 calculates Z₀ and φ at at least two differentfrequency f1, f2 and calculates the imaginary part Im{Z(f)} at each ofthese frequencies based onIm{Z(f)}=Z ₀·sin(φ)  (21).The complex gain A may be dependent on the frequency, that is, A₀=A₀(f)and φ₀=φ₀(f). In this case, A₀(f) and φ₀(f) may be obtained in acalibration routine for each of the at least two frequencies f₁, f₂ andstored in the control and calculation circuit 27. The control andcalculation circuit 27 then, for example, uses A₀(f1) and φ₀(f1) tocalculate Z₀(f1) and φ(f1) based on equations (20a) and (20b) and A₀(f2)and φ₀(f2) to calculate Z₀(f2) and φ(f2) based on equations (20a) and(20b). The calibration routine may include connecting an ohmic resistorwith a resistance R₀ instead of a battery to the temperature detectioncircuit 2. Signals s26 _(I)′(f,t) and s26 _(Q)′(f,t) explained withreference to equations (18a) and (18b) are then given bys26_(I)′(f,t)=V _(I) ′=A ₀ ·R ₀·cos(φ₀)  (22a)s26_(Q)′(f,t)=V _(Q) ′=A ₀ ·R ₀·sin(φ₀)  (22b).Based on these signals s26 _(I)′(f,t) and s26 _(Q)′(f,t) magnitude A₀and phase φ₀ of the complex amplification may be calculated by

$\begin{matrix}{A_{0} = \frac{\sqrt{\left( V_{I}^{\prime} \right)^{2} + \left( V_{Q}^{\prime} \right)^{2}}}{R_{0}}} & \left( {23a} \right) \\{\varphi_{0} = {{\arctan\left( \frac{V_{Q}^{\prime}}{V_{I}^{\prime}} \right)}.}} & \left( {23b} \right)\end{matrix}$

Although equations (15a) to (23b) illustrate/explain a method ofdetecting the imaginary part of the battery resistance based on asinusoidal input current i(f,t) the method is not restricted to asinusoidal input current, but any other type of alternating inputcurrent, such as a rectangular input current may be used as well. Ineach case the second and third alternating signals s2(ωt) and s1′(ωt)can be sinusoidal signals, such as s2(ωt)=cos(ωt) and s1′(ωt)=sin(ωt).

FIG. 9 shows a modification of the temperature detection circuit 2 shownin FIG. 8. Besides measuring the voltage v(f,t) across the battery 1 thetemperature detection circuit 2 shown in FIG. 9 also measures the inputcurrent i(f,t). For this, a current sense resistor 30 is connected inseries with the modulator 22. A sense voltage v30(f,t) across theresistor is proportional to the input current i(f,t),v30(f,t)=R ₃₀ ·i(f,t)  (24),where R₃₀ is a resistance of the sense resistor. The sense voltagev30(f,t) is processed in the same way as the battery voltage v(f,t).That is, a further sense amplifier 24 ₂ receives the sense voltagev30(f,t) and provides a further measurement signal m2(f,t). A thirdmodulator 2512 modulates the further measurement signal m2(f,t) with thethird alternating signal s1′(ωt) and a fourth modulator 25 _(Q2)modulates the further measurement signal m2(f,t) with the secondalternating signal s2(ωt). An output signal s25 _(I2)(f,t) of the thirdmodulator 2512 is filtered by a third low pass filter 26 _(I2), and anoutput signal s25 _(Q2)(f,t) of the fourth modulator 25 _(Q2) isfiltered by a fourth low pass filter 26 _(Q2). Based on what isexplained in context with equations (17a) and (17b) above it can beshown that the output signals (output values) of the first to fourth lowpass filters 26 _(I), 26 _(Q), 26 _(I2), 26 _(Q2) are as follows:

$\begin{matrix}{V_{I} = {\frac{A_{0} \cdot Z_{0} \cdot I_{0}}{2}{\cos\left( {\varphi_{0} + \varphi} \right)}}} & \left( {25a} \right) \\{V_{Q} = {\frac{A_{0} \cdot Z_{0} \cdot I_{0}}{2}{\sin\left( {\varphi_{0} + \varphi} \right)}}} & \left( {25b} \right) \\{V_{I\; 2} = {\frac{A_{02} \cdot R_{30} \cdot I_{0}}{2}{\cos\left( \varphi_{02} \right)}}} & \left( {25c} \right) \\{V_{Q\; 2} = {\frac{A_{02} \cdot R_{30} \cdot I_{0}}{2}{\sin\left( \varphi_{02} \right)}}} & \left( {25d} \right)\end{matrix}$According to one example, the sense amplifiers 24, 24 ₂ are senseamplifiers of the same type with the same complex gain, so that A₀₂=A₀and φ₀=φ₀₂. In this case, A₀ and φ₀ can be calculated by the control andcalculation circuit 27 based on V_(I2) and V_(Q2) as follows:

$\begin{matrix}{A_{0} = {A_{02} = {2 \cdot \frac{\sqrt{\left( V_{I\; 2} \right)^{2} + \left( V_{Q\; 2} \right)^{2}}}{R_{30} \cdot I_{0}}}}} & \left( {23a} \right) \\{\varphi_{0} = {\varphi_{02} = {{\arctan\left( \frac{V_{Q\; 2}}{V_{I\; 2}} \right)}.}}} & \left( {23b} \right)\end{matrix}$Thus, in this example, a calibration routine is not required but A₀ andφ₀ are calculated by the control and calculation circuit 27 during thetemperature measurement operation of the temperature detection circuit27. Further, control and calculation circuit 27 calculates the imaginarypart of the battery impedance Z(f) at each of the at least twofrequencies based on equations (20a), (20b), and (21).

Referring to FIG. 10, the battery 1 explained before may be part of abattery arrangement with a plurality of batteries 1, 1 _(I), 1 _(II)connected in series. A temperature detection circuit 2, 2 _(I), 2 _(II)may be connected to each of these batteries, wherein each of thesetemperature detection circuits 2, 2 _(I), 2 _(II) is configured todetect the temperature of the battery 1, 1 _(I), 1 _(II) it is connectedto.

FIG. 11 shows a modification of the arrangement shown in FIG. 10. In thearrangement shown in FIG. 11 there is only one temperature detectioncircuit 2 and a multiplexer 3. The multiplexer 3 is connected betweenthe battery arrangement with the plurality of batteries 1, 1 _(I), 1_(II) and the temperature detection circuit 2. This multiplexer 3 isconfigured, at each time, to connect the temperature detection circuitwith one of the several batteries 1, 1 _(I), 1 _(II) and, in a timelysuccessive fashion, connect the individual batteries 1, 1 _(I), 1 _(II)of the arrangement to the temperature detection circuit 2. By this, thetemperature detection circuit 2 in a timely successive fashion detectsthe temperatures of the individual batteries 1, 1 _(I), 1 _(II) of thebattery arrangement.

FIG. 12 shows a battery arrangement with a plurality of batteries 1_(I), 1, 1 _(II) connected in series and a temperature detection circuit2 according to another example. The temperature detection circuit shownin FIG. 12 is configured to drive one input current i(f,t) at at leasttwo different frequencies f₁, f₂ into the battery series circuit,measure the voltage v_(I)(f,t), v(f,t), v_(II)(f,t) across each battery1 _(I), 1, 1 _(II), and detect a temperature of each battery v_(I)(f,t),v(f,t), v_(II)(f,t) based on the measured voltage v_(I)(f,t), v(f,t),v_(II)(f,t) in accordance with any of the methods explained before.

The following examples may illustrate one or more aspects of thedisclosure.

Example 1

A method, including: driving an alternating input current with a firstfrequency into a battery and detecting an imaginary part of a batteryimpedance at the first frequency; driving an alternating current with asecond frequency different from the first frequency into the battery anddetecting an imaginary part of the battery impedance at the secondfrequency; and calculating an intercept frequency at which the imaginarypart equals a predefined value at least based on the imaginary partobtained at the first frequency and the imaginary part obtained at thesecond frequency.

Example 2

The method of example 1, wherein the predefined value is zero.

Example 3

The method of example 1 or 2, wherein the predefined value is differentfrom zero.

Example 4

The method of any combination of examples 1 to 3, further including:obtaining temperature information from a look-up table that includes aplurality of frequency-temperature information pairs.

Example 5

The method of any combination of examples 1 to 4, wherein calculatingthe intercept frequency includes: calculating a straight line based onthe imaginary part obtained at the first frequency and the imaginarypart obtained at the second frequency; and calculating the frequency atwhich the calculated straight line intercepts the predefined value.

Example 6

The method of any combination of examples 1 to 5, wherein detecting theimaginary part at each of the first and second frequencies includes:measuring a voltage across the battery to obtain a measurement signal;demodulating the measurement signal to obtain a demodulated measurementsignal; and low pass filtering the demodulated measurement signal.

Example 7

The method of example 6, wherein detecting the imaginary part at each ofthe first and second frequencies further includes: measuring thealternating input current to obtain a further measurement signal;detecting a phase shift based on the further measurement signal; anddetecting the imaginary part based on the measured voltage and thedetected phase shift.

Example 8

The method of example 6 or 7, further including performing a calibrationroutine before detecting the imaginary part at each of the first andsecond frequencies, wherein the calibration routine includes detecting aphase shift, and

wherein detecting the imaginary part comprises detecting the imaginarypart based on the measured voltage and the detected phase shift.

Example 9

The method of any combination of examples 6 to 8, wherein demodulatingthe measurement signal comprises multiplying the measurement signal witha sinusoidal signal.

Example 10

The method of example 9, wherein a phase shift between the alternatinginput current and the sinusoidal signal is 90°.

Example 11

The method of any combination of examples 6 to 10, wherein demodulatingthe measurement signal includes: multiplying the measurement signal witha first sinusoidal signal; and multiplying the measurement signal with asecond sinusoidal signal, wherein a phase shift between the firstsinusoidal signal and the second sinusoidal signal is 90°.

Example 12

The method of any combination of examples 1 to 11, further including:driving, at least once, an alternating current with a further frequencydifferent from the first frequency and the second frequency into thebattery and detecting an imaginary part of the battery impedance at thefurther frequency, so as to obtain an imaginary part at at least onefurther frequency; and calculating the intercept frequency additionallybased on the imaginary part obtained at the at least one furtherfrequency.

Example 13

The method of example 12, wherein calculating the intercept frequencyincludes calculating a linear function based on a least square method.

Example 14

The method of example 12, wherein calculating the intercept frequencyincludes calculating a non-linear function.

Example 15

The method of any combination of examples 1 to 14, wherein the batteryincludes at least one battery cell.

Example 16

The method of example 15, wherein the battery includes two or morebattery cells connected in series.

Example 17

The method of example 15, wherein the battery includes two or morebattery cells connected in parallel.

Example 18

The method of any combination of examples 1 to 17, wherein at least oneadditional battery is connected in series with the battery.

Example 19

A temperature detection circuit configured to drive an alternatingcurrent with a first frequency into a battery and detect an imaginarypart of a battery impedance at the first frequency; drive an alternatingcurrent with a second frequency different from the first frequency intothe battery and detect an imaginary part of the battery impedance at thesecond frequency; and calculate an intercept frequency at which theimaginary part equals a predefined value at least based on the imaginarypart obtained at the first frequency and the imaginary part obtained atthe second frequency.

Example 20

The temperature detection circuit of example 19, wherein the predefinedvalue is zero.

Example 21

The temperature detection circuit of example 19, wherein the predefinedvalue is different from zero.

Example 22

The temperature detection circuit of any combination of examples 19 to21, wherein the temperature detection circuit is further configured toobtain temperature information from a look-up table that includes aplurality of frequency-temperature information pairs.

Example 23

The temperature detection circuit of any combination of examples 19 to22, wherein the temperature detection circuit is configured to calculatethe intercept frequency using the steps of calculating a straight linebased on the imaginary part obtained at the first frequency and theimaginary part obtained at the second frequency; and calculating thefrequency at which the calculated straight line intercepts thepredefined value.

Example 24

The temperature detection circuit of any combination of examples 19 to23, wherein the temperature detection circuit is configured to detectthe imaginary part at each of the first and second frequencies using thesteps of measuring a voltage across the battery to obtain a measurementsignal; demodulating the measurement signal to obtain a demodulatedmeasurement signal; and low pass filtering the demodulated measurementsignal.

Example 25

The temperature detection circuit of example 24, wherein the temperaturedetection circuit is configured to detect the imaginary part at each ofthe first and second frequencies further using the steps of measuringthe alternating input current to obtain a further measurement signal;detecting a phase based on the further measurement signal; and detectingthe imaginary part based on the measured voltage and the detected phaseshift.

Example 26

The temperature detection circuit of example 24 or 25, wherein thetemperature detection circuit is further configured to perform acalibration routine before detecting the imaginary part at each of thefirst and second frequencies, wherein the calibration routine includesdetecting a phase, and wherein detecting the imaginary part includesdetecting the imaginary part based on the measured voltage and thedetected phase shift.

Example 27

The temperature detection circuit of any combination of examples 19 to26, wherein demodulating the measurement signal includes multiplying themeasurement signal with a sinusoidal signal.

Example 28

The temperature detection circuit of example 27, wherein a phase shiftbetween the alternating input current and the sinusoidal signal is 90°.

Example 29

The method of any combination of examples 19 to 28, wherein demodulatingthe measurement signal includes: multiplying the measurement signal witha first sinusoidal signal; and multiplying the measurement signal with asecond sinusoidal signal, wherein a phase shift between the firstsinusoidal signal and the second sinusoidal signal is 90°.

Example 30

The temperature detection circuit of any combination of examples 19 to29, wherein the temperature detection circuit is further configured todrive, at least once, an alternating current with a further frequencydifferent from the first frequency and the second frequency into thebattery and detecting an imaginary part of the battery impedance at thefurther frequency, so as to obtain an imaginary part at at least onefurther frequency; and calculate the intercept frequency additionallybased on the imaginary part obtained at the at least one furtherfrequency.

Example 31

The temperature detection circuit of example 30, wherein calculating theintercept frequency includes calculating a linear function based on aleast square method.

Example 32

The temperature detection circuit of example 30, wherein calculating theintercept frequency includes calculating a non-linear function.

Although various exemplary embodiments of the invention have beendisclosed, it will be apparent to those skilled in the art that variouschanges and modifications can be made which will achieve some of theadvantages of the invention without departing from the spirit and scopeof the invention. It will be obvious to those reasonably skilled in theart that other components performing the same functions may be suitablysubstituted. It should be mentioned that features explained withreference to a specific figure may be combined with features of otherfigures, even in those cases in which this has not explicitly beenmentioned. Further, the methods of the invention may be achieved ineither all software implementations, using the appropriate processorinstructions, or in hybrid implementations that utilize a combination ofhardware logic and software logic to achieve the same results. Suchmodifications to the inventive concept are intended to be covered by theappended claims.

Spatially relative terms such as “under,” “below,” “lower,” “over,”“upper” and the like, are used for ease of description to explain thepositioning of one element relative to a second element. These terms areintended to encompass different orientations of the device in additionto different orientations than those depicted in the figures. Further,terms such as “first,” “second” and the like, are also used to describevarious elements, regions, sections, etc. and are also not intended tobe limiting. Like terms refer to like elements throughout thedescription.

As used herein, the terms “having,” “containing,” “including,”“comprising” and the like are open ended terms that indicate thepresence of stated elements or features, but do not preclude additionalelements or features. The articles “a,” “an” and “the” are intended toinclude the plural as well as the singular, unless the context clearlyindicates otherwise.

With the above range of variations and applications in mind, it shouldbe understood that the present invention is not limited by the foregoingdescription, nor is it limited by the accompanying drawings. Instead,the present invention is limited only by the following claims and theirlegal equivalents.

The invention claimed is:
 1. A method comprising: driving an alternatinginput current with a first frequency into a battery, the first frequencyhaving a first predetermined value, and detecting a first imaginary partof an impedance of the battery at the first frequency; driving thealternating input current with a second frequency into the battery, thesecond frequency having a second predetermined value different from thefirst predetermined value of the first frequency, and detecting a secondimaginary part of the impedance of the battery at the second frequency;and calculating, by a control and calculation circuit, an interceptfrequency at which a third imaginary part of the impedance of thebattery at the intercept frequency equals a predefined value at leastbased on the first imaginary part of the impedance of the battery at thefirst frequency and the second imaginary part of the impedance of thebattery at the second frequency.
 2. The method of claim 1, wherein thepredefined value is zero.
 3. The method of claim 1, wherein thepredefined value is different from zero.
 4. The method of claim 1,further comprising obtaining temperature information from a look-uptable that includes a plurality of frequency-temperature informationpairs.
 5. The method of claim 1, wherein calculating the interceptfrequency comprises: calculating a straight line based on the firstimaginary part of the impedance of the battery at the first frequencyand the second imaginary part of the impedance of the battery at thesecond frequency; and calculating the intercept frequency at which thecalculated straight line intercepts the predefined value.
 6. The methodof claim 1, wherein detecting the first imaginary part of the impedanceof the battery and the second imaginary part of the impedance of thebattery at each of the first and second frequencies comprises: measuringa voltage across the battery to obtain a measurement signal;demodulating the measurement signal to obtain a demodulated measurementsignal; and low pass filtering the demodulated measurement signal. 7.The method of claim 6, wherein detecting the first imaginary part of theimpedance of the battery and the second imaginary part of the impedanceof the battery at each of the first and second frequencies furthercomprises: measuring the alternating input current to obtain a furthermeasurement signal; detecting a phase shift based on the furthermeasurement signal; and detecting the respective imaginary part of theimpedance of the battery based on the measured voltage and the detectedphase shift.
 8. The method of claim 6, further comprising performing acalibration routine before detecting the first imaginary part of theimpedance of the battery and the second imaginary part of the impedanceof the battery at each of the first and second frequencies, wherein thecalibration routine comprises detecting a phase shift, and whereindetecting the respective imaginary part of the impedance of the batterycomprises detecting the imaginary part of the impedance of the batterybased on the measured voltage and the detected phase shift.
 9. Themethod of claim 6, wherein demodulating the measurement signal comprisesmultiplying the measurement signal with a sinusoidal signal.
 10. Themethod of claim 9, wherein a phase shift between the alternating inputcurrent and the sinusoidal signal is 90°.
 11. The method of claim 6,wherein demodulating the measurement signal comprises: multiplying themeasurement signal with a first sinusoidal signal; and multiplying themeasurement signal with a second sinusoidal signal, wherein a phaseshift between the first sinusoidal signal and the second sinusoidalsignal is 90°.
 12. The method of claim 1, further comprising: driving,at least once, the alternating input current with a further frequencyinto the battery, the further frequency having a further predeterminedvalue different from the first predetermined value of the firstfrequency and the second predetermined value of the second frequency,and detecting a further imaginary part of the impedance of the batteryat the further frequency; and wherein the intercept frequency is furthercalculated based on the further imaginary part of the impedance of thebattery at the further frequency.
 13. The method of claim 12, whereincalculating the intercept frequency comprises calculating a linearfunction based on a least square method.
 14. The method of claim 12,wherein calculating the intercept frequency comprises calculating anon-linear function.
 15. The method of claim 1, wherein the batterycomprises at least one battery cell.
 16. The method of claim 15, whereinthe battery comprises two or more battery cells connected in series. 17.The method of claim 15, wherein the battery comprises two or morebattery cells connected in parallel.
 18. The method of claim 1, whereinat least one additional battery is connected in series with the battery.19. A temperature detection circuit comprising a control and calculationcircuit, wherein the temperature detection circuit is configured to:drive an alternating current with a first frequency into a battery, thefirst frequency having a first predetermined value, and detect a firstimaginary part of an impedance of the battery at the first frequency;and drive the alternating current with a second frequency into thebattery, the second frequency having a second predetermined valuedifferent from the first predetermined value of the first frequency, anddetect a second imaginary part of the impedance of the battery at thesecond frequency, wherein the control and calculation circuit isconfigured to calculate an intercept frequency at which a thirdimaginary part of the impedance of the battery at the interceptfrequency equals a predefined value at least based on the firstimaginary part of the impedance of the battery at the first frequencyand the second imaginary part of the impedance of the battery at thesecond frequency.
 20. The temperature detection circuit of claim 19,wherein the predefined value is zero.
 21. The temperature detectioncircuit of claim 19, wherein the predefined value is different fromzero.
 22. The temperature detection circuit of claim 19, wherein thetemperature detection circuit is further configured to obtaintemperature information from a look-up table that includes a pluralityof frequency-temperature information pairs.
 23. The temperaturedetection circuit of claim 19, wherein the temperature detection circuitis configured to calculate the intercept frequency using the steps of:calculating a straight line based on the first imaginary part of theimpedance of the battery at the first frequency and the second imaginarypart of the impedance of the battery at the second frequency; andcalculating the intercept frequency at which the calculated straightline intercepts the predefined value.
 24. The temperature detectioncircuit of claim 19, wherein the temperature detection circuit isconfigured to detect the first imaginary part of the impedance of thebattery and the second imaginary part of the impedance of the battery ateach of the first and second frequencies using the steps of: measuring avoltage across the battery to obtain a measurement signal; demodulatingthe measurement signal to obtain a demodulated measurement signal; andlow pass filtering the demodulated measurement signal.
 25. Thetemperature detection circuit of claim 24, wherein the temperaturedetection circuit is configured to detect the first imaginary part ofthe impedance of the battery and the second imaginary part of theimpedance of the battery at each of the first and second frequenciesfurther using the steps of: measuring the alternating current to obtaina further measurement signal; detecting a phase based on the furthermeasurement signal; and detecting the respective imaginary part of theimpedance of the battery based on the measured voltage and the detectedphase shift.
 26. The temperature detection circuit of claim 24, whereinthe temperature detection circuit is further configured to perform acalibration routine before detecting the first imaginary part of theimpedance of the battery and the second imaginary part of the impedanceof the battery at each of the first and second frequencies, wherein thecalibration routine comprises detecting a phase, and wherein detecting arespective imaginary part of the impedance of the battery comprisesdetecting the respective imaginary part of the impedance of the batterybased on the measured voltage and the detected phase shift.
 27. Thetemperature detection circuit of claim 24, wherein demodulating themeasurement signal comprises multiplying the measurement signal with asinusoidal signal.
 28. The temperature detection circuit of claim 27,wherein a phase shift between the alternating current and the sinusoidalsignal is 90°.
 29. The temperature detection circuit of claim 24,wherein demodulating the measurement signal comprises: multiplying themeasurement signal with a first sinusoidal signal; and multiplying themeasurement signal with a second sinusoidal signal, wherein a phaseshift between the first sinusoidal signal and the second sinusoidalsignal is 90°.
 30. The temperature detection circuit of claim 19,wherein the temperature detection circuit is further configured todrive, at least once, the alternating current with a further frequencyinto the battery, the further frequency having a further predeterminedvalue different from the first predetermined value of the firstfrequency and the second predetermined value of the second frequency,and detect a further imaginary part of the impedance of the battery atthe further frequency, and wherein the control and calculation circuitis further configured to calculate the intercept frequency based on theimaginary part of the impedance of the battery at the further frequency.31. The temperature detection circuit of claim 30, wherein the controland calculation circuit is configured to calculate the interceptfrequency by calculating a linear function based on a least squaremethod.
 32. The temperature detection circuit of claim 30, wherein thecontrol and calculation circuit is configured to calculate the interceptfrequency by calculating a non-linear function.